Directly from JetBlue's website:
Same-Day Flight Change
Cities with Multiple Flights a Day- You must contact JetBlue prior to the departure of your original flight
- You can make your confirmed same-day changes online, via 1-800-JETBLUE (538-2583) or at the airport beginning at midnight (in the time zone of the departing flight) of the same calendar day as your original scheduled flight.
- You must travel on an earlier or later flight the same day.
- You must travel between the same city pairs or designated co-located airport.
- A same-day change fee of $75 may apply, depending on your fare.
Cities with One Flight a DayThe same-day change option is not available for cities with one flight a day.
Additional Mosaic Same-Day Change Benefits- You can make your confirmed same-day changes via the dedicated Mosaic line or at the airport beginning a full 24 hours (in the time zone of the departing flight) prior to your original scheduled flight.
- Same day change fee is waived.
- All other same-day change guidelines apply.
There is no mention that the fee waiver does not apply to Mint fares, so going by the company's own verbiage, I would surmise that the agent you spoke with was mistaken.
Additionally, even as a non-Mosaic, the SDC fee is $75 with no mention of a re-fare.